New constraints on Yukawa-type interactions from the Casimir effect V. M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, Moscow, Russia

New constraints

on Yukawa-type interactions from the Casimir effect

V. M. Mostepanenko

Noncommercial Partnership “Scientific Instruments”, Moscow, Russia

QFEXT11, Benasque, Spain, 2011

CONTENT

1. Introduction2. Constraints from gravitational experiments3. Constraints from the normal Casimir force between test bodies with smooth surfaces4. Constraints from the normal Casimir force between test bodies with corrugated surfaces5. Constraints from the lateral Casimir force6. Constraints from the thermal Casimir-Polder force7. Possibilities to strengthen constraints from the Casimir force8. Conclusions


1. INTRODUCTION

Yukawa-type corrections to Newton’s law:

Power-type corrections to Newton’s law:


Yukawa- and power-type potentials originate from:

1) Exchange of light and massless elementary particles, such as:

--- arion; --- scalar axion; --- graviphoton; --- dilaton; --- goldstino; --- moduli.

These particles may contribute to the dark matter and dark energy.


2) Extra-dimensional theories with low-energy compactification scale

Arkani-Hamed, Dimopoulos, Dvali, PRD, 1999

cm


The Yukawa-type force between two macrobodies


2. CONSTRAINTS FROM GRAVITATIONAL

EXPERIMENTS

The strongest constraints on Yukawa-type corrections to Newton's gravitational law following from various gravitational experiments (lines 1-5)and measurements of the Casimir force (line 6).


3. CONSTRAINTS FROM THE NORMAL CASIMIR FORCE BETWEEN TEST BODIES WITH SMOOTH SURFACES

Measured quantities are the Casimir force or its gradient:

Obtaining constraints on Yukawa forces:


Opinion: one and the same experiment cannot be used for the two purposes

(a) to exclude or confirm some theory of the Casimir force;

(b) to place constraints on the Yukawa force

(Lambrecht, Reynaud, arXiv:1106.3848)

This opinion would be worthwhile only if the difference between the excluded and confirmed theories for the Casimir force can be modeled by the Yukawa force.


Measurements of the Casimir force usingan atomic force microscope

Force sensitivity 10-17 N possible

We achieve 10-13N

Mohideen et al, 1998-2000


Shematic setup

Schematic setup with a micromachined oscillatorfor measurements of the Casimir force gradient

Decca et al, 2003-2007QFEXT11, Benasque, Spain, 2011

The strongest constraints on Yukawa-type correctionsto Newton's gravitational law

obtained from the measurementof the Casimir force using an atomic force microscope (red line), from the measurement of the Casimir pressure by means of a micromachined oscillator (green line), and from the Casimir-lessexperiment (blue line), from the torsion pendulum experimentof 1997 (grey line) and from thetorsion balance experiment 2009(black line).


Constraints from recent torsion pendulum experiment

(Sushkov, Kim, Dalvit, Lamoreaux, Nature Phys. 2011; arXiv:1108.2547)

Problems with this experiment:

(a) The original data are not available; (b) the measured force of nonestablished origin is up to a factor of 10 larger than the Casimir force; (c) at separations above 3 micrometers the Casimir force obtained after subtraction much better agrees not with the Drude, but with the plasma model

(Klimchitskaya, Bordag, Fischbach, Krause, Mostepanenko, Int. J. Mod. Phys. A, 2011)


Constraints on Yukawa-type interaction obtained from the Casimir-lessexperiment (blue line), Lamoreaux, 1997 experiment[Bordag, Geyer, Klimchitskaya,Mostepanenko, PRD, 1998] (grey line),Lamoreaux, 2011 experiment (pink line) , gravitational experiment [Geraci et al.,PRD 2008] (dashed line).


Problems arising from using large spherical lenses cast doubts on all constraints obtained from Lamoreaux’s and Masuda&Sasaki experiments.

4. CONSTRAINTS FROM THE NORMAL CASIMIR FORCE BETWEEN TEST BODIES WITH CORRUGATED SURFACES

(Bao, Guerout, Lussange, Lambrecht, Cirelli, Klemens, Mansfield, Pai, Chan, PRL, 2010)


Constraints on the parameters of Yukawa-type interactionwhich are obtained from the experiments performedby means of a micromechanical torsional oscillator with a corrugated Si plate (pink line) and with a flat Au-coated plate (greenline), from the Casimir-less experiment (blue line), and from the experiments using a torsion pendulum (grey and black lines).

Bezerra, Klimchitskaya, Mostepanenko, Romero,PRD, 2011


5. CONSTRAINTS

FROM THE LATERAL CASIMIR FORCE

Golestanian, Kardar, PRL 1997;Chen, Mohideen, Klimchitskaya, Mostepanenko, PRL 2002, PRA 2002;

Chiu, Klimchitskaya, Marachevsky, Mostepanenko, Mohideen, PRB 2009, PRB 2010.


Experimental scheme

x-piezo introduces phase changez-piezo changes separation distance


Constraints on the parameters of Yukawa-type interaction

from measurements of the lateral Casimir force between corrugated surfaces (red line), and from measurements of the normal Casimir force by means of an atomic force microscope (red dashed line), and a micromachined oscillator(green line).

Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD, 2010


6. CONSTRAINTS FROM THE THERMAL CASIMIR-POLDER FORCE

Obrecht, Wild, Antezza, Pitaevskii, Stringari, Cornell, PRL (2007)

Experiment on measuring the Casimir-Polder forcebetween a glass plate and Rb atoms belonging tothe Bose-Einstein condensate.


Obrecht, Wild, Antezza, Pitaevskii, Stringari, Cornell, PRL (2007);Klimchitskaya, Mostepanenko, JPA (2008).

Frequency shift of center-of-mass oscillations of Bose-Einstein condensate of Rb atoms


Constraints from measurementsof the Casimir-Polder force (brown line), from the experiment using a torsion balance (black line), from the measurement of the Casimir force by means of a torsion pendulum (grey line), and from the gravitationalexperiment (short-dashed line).

(Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD 2010)


7. POSSIBILITIES TO STRENGTHEN

CONSTRAINTS FROM THE CASIMIR FORCE

1. Using normal Casimir force with a smooth sphere and a corrugated plate.

2. Using normal Casimir force in cylinder-plate configuration.


Plate with rectangular corrugations

Bezerra, Klimchitskaya, Mostepanenko, Romero,PRD, 2011

The dashed line shows the prospective constraintsthat can be obtained from the experiment with acorrugated Au plateinstead of Si plate.


Constraints on the parameters of Yukawa-type interaction

from proposed measurements of the normal Casimir force between a smooth sphere and a corrugated plate of micromachined oscallator(dashed green line),

from measurements of the lateral Casimir force between corrugatedsurfaces (red line),

and from measurements of thenormal Casimir force using asmooth plate of micromachined oscillator (green line).

Bezerra, Klimchitskaya, Mostepanenko, Romero, PRD 2010


Cylinder-plate configuration

Decca, Fischbach, Klimchitskaya, Krause, Lopez, Mostepanenko, PRA 2010


The dashed line showsthe prospective constraints that can be obtained from measuring the gradient of the Casimir force between a plate and a microfabricatedcylinder.

Klimchitskaya, Romero, PRD 2010


8. CONCLUSIONS 1. Experiments on the Casimir force lead to stronger constraints at shorter interaction range where gravitational experiments do not work.

2. Recent measurements of the normal Casimir force between a sphere and rectangular corrugated plate confirmed constraints obtained from several different experiments.

3. Precise measurements of the lateral Casimir force strengthen previously known constraints up to two and a half million times.

4. In near future further strengthening of constraints is expected from measuring the normal Casimir force between a smooth sphere and a corrugated plate.


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New constraints on Yukawa-type interactions from the Casimir effect V. M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, Moscow, Russia